Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  while (scanf("%d", &n) != EOF) {
    n = 2 * n;
    int mid = (int)sqrt(n * 1.0) + 1;
    bool flg = false;
    for (int i = 1; i <= mid; i++) {
      int t = n - i * (i + 1);
      if (t <= 0) continue;
      int tt = (int)sqrt(t * 1.0) - 1;
      for (int j = 0; j < 3; j++) {
        if (t == (tt + j) * (tt + j + 1)) flg = true;
      }
    }
    if (flg)
      printf("YES\n");
    else {
      printf("NO\n");
    }
  }
  return 0;
}